Saturday, June 11, 2016

Are Global Temperature Anomalies Normally Distributed?

There is some discussion elsewhere here about what weather and climate numbers are normally dististributed and what aren't.

I don't know if one can say a priori if a normal distribution is expected. But the fact is many sets of numbers from different fields are normally dististributed, but many aren't.

There are statistical tests for normalcy that you can apply to your data, which I'm not going to do here. I'll just present two plots.

The first is the average daily temperature in my town of Salem, Oregon. I've been collecting it daily since I moved here in September 2012, and was able to easily obtain the numbers for the 12 months prior. Here's a histogram of the distribution of the day's deviation from average (defined over the interval 1981-2010).

The bins are 0.5°F wide, and instead of plotting the count of the number of temperatures in each bin I've plotted the percentage of them amount the total. It looks fairly Gaussian (="normal"), but with the peak count shifted a couple of degrees to the right, which I assume is global warming.

Then I've plotted the monthly anomalies for HadCRUT4 over the length of their record, which starts in January 1850 (6/12 8:30 am PT: this has been corrected since the original last night; the results didn't change sustantially):

These data clearly aren't normally distributed. The long length of the record, most of which is before the sharp change in manmade global warming in 1975 or so, skews the dataset.

It's late and I'll try to write more about this tomorrow. Corrections and comments welcome.


Unknown said...

The skewed distribution does appear to be what would be expected if global mean temps were increasing.

Would it be possible to "restore" the normal distribution by, say, detrending the data or something like that? I do not know if that would prove anything much, other than show the temperature distribution is indeed normal.

JoeT said...

Thanks for this post David. A couple of points I would make:

1- I don't think you need to do a statistical test for a blog post, but it would get the point across it you simply fit a normal distribution to the data and we can see how close the data is to the fit. This would get across the idea that in science we often just say, let's assume a gaussian distribution. On the other hand if there is significant skewness in the data, we can then go on to study that.

2- Richard calculated the mean and 1 sigma for the YEARLY Hadcrut4 data. If you're so inclined, maybe you can plot the pdf for the yearly data and show whether that looks anything like a normal distribution.

3- I was curious about the problem I raised in the earlier thread, can we estimate when we might see a few fatal wet bulb temperature days in the Iran, India, Pakistan regions? It's not even clear to me that wet bulb temperatures follow a normal distribution. For example, the relative humidity may not stay constant, but instead increase drastically since SST temperatures in the region are increasing at a phenomenal rate. As it turns out, someone of course already considered this problem here. The results show that with a B-A-U scenario, major parts of the region may be uninhabitable by the end of the century.

David Appell said...

Joe, by fitting a normal distribution to the histogram, do you mean simply plotting that function using the mean and standard deviation of the data?

JoeT said...

David, I use Matlab at work to analyze data. I was thinking along the lines of keeping the mean and standard deviation as free variables and then do a chi-squared minimization with respect to the data. With Matlab you can do this problem very easily. If you are using Excel, what you suggested would work nicely instead.